Answer :
To solve the expression [tex]\(\left(\left(-\frac{1}{7}\right)^3\right)^{-3}\)[/tex], let's break it down step by step:
1. Calculate the inner exponentiation:
[tex]\[ \left(-\frac{1}{7}\right)^3 \][/tex]
Raising [tex]\(-\frac{1}{7}\)[/tex] to the power of 3:
[tex]\[ \left(-\frac{1}{7}\right)^3 = -\frac{1}{7} \times -\frac{1}{7} \times -\frac{1}{7} = -\frac{1}{343} \][/tex]
So, the intermediate result here is approximately [tex]\(-0.0029154518950437313\)[/tex].
2. Raise this result to the power of -3:
[tex]\[ \left(-\frac{1}{343}\right)^{-3} \][/tex]
Using the property of exponents [tex]\(a^{-n} = \frac{1}{a^n}\)[/tex]:
[tex]\[ \left(-\frac{1}{343}\right)^{-3} = \left(\frac{1}{-\frac{1}{343}}\right)^3 = (-343)^3 \][/tex]
3. Now, evaluate [tex]\((-343)^3\)[/tex]:
[tex]\[ (-343)^3 = -343 \times -343 \times -343 = -40353607 \][/tex]
This evaluates to
So, the final value of [tex]\(\left(\left(-\frac{1}{7}\right)^3\right)^{-3}\)[/tex] is [tex]\( -40353607 \)[/tex].
Therefore, among the given choices, the correct answer is:
[tex]\[ \boxed{-40,353,607} \][/tex]
1. Calculate the inner exponentiation:
[tex]\[ \left(-\frac{1}{7}\right)^3 \][/tex]
Raising [tex]\(-\frac{1}{7}\)[/tex] to the power of 3:
[tex]\[ \left(-\frac{1}{7}\right)^3 = -\frac{1}{7} \times -\frac{1}{7} \times -\frac{1}{7} = -\frac{1}{343} \][/tex]
So, the intermediate result here is approximately [tex]\(-0.0029154518950437313\)[/tex].
2. Raise this result to the power of -3:
[tex]\[ \left(-\frac{1}{343}\right)^{-3} \][/tex]
Using the property of exponents [tex]\(a^{-n} = \frac{1}{a^n}\)[/tex]:
[tex]\[ \left(-\frac{1}{343}\right)^{-3} = \left(\frac{1}{-\frac{1}{343}}\right)^3 = (-343)^3 \][/tex]
3. Now, evaluate [tex]\((-343)^3\)[/tex]:
[tex]\[ (-343)^3 = -343 \times -343 \times -343 = -40353607 \][/tex]
This evaluates to
So, the final value of [tex]\(\left(\left(-\frac{1}{7}\right)^3\right)^{-3}\)[/tex] is [tex]\( -40353607 \)[/tex].
Therefore, among the given choices, the correct answer is:
[tex]\[ \boxed{-40,353,607} \][/tex]
